Question

If the selling price of 50 articles is equal to the cost price of 40 articles then the loss and gain percent is
a. 20% gain
b. 20% loss
c. 25% loss
d. 25% gain

Answer 1

Hint:We will assume the cost price of an article to be Rs. 1 and we have 40 articles, so the total cost price of 40 articles will be Rs. 40 and this Rs. 40 will be equal to the selling price of 50 articles, according to the condition given in the question and then we will solve the question further. To solve this question, we should know the formulas, loss = (cost price – selling price), profit = (selling price – cost price), $ \text{loss}\%=\dfrac{\text{loss}}{\text{cost price}}\times 100 $ and $ \text{gain}\%=\dfrac{\text{gain}}{\text{cost price}}\times 100 $ .

Complete step-by-step answer:
It is given in the question that the selling price of 50 articles is equal to the cost price of 40 articles and we have been asked to find the loss and gain percentage. Let us assume that the cost of one article is Rs. 1, so we will get the cost price of 40 articles as $ 40\times 1=Rs.40 $ .
Now, we have been given the question that selling price of 50 articles is equal to the cost price of 40 articles, which is Rs. 40. So we can say that the selling price of 50 articles is equal to Rs. 40. Therefore, we get the cost price of 50 articles as $ 50\times 1=Rs.50 $ .
So, we can see that the cost price of 50 articles is greater than the selling price of 50 articles, that is 50 > 40. Thus we can say that there will be a loss. So, we can find the loss as,
Loss = (cost price – selling price)
Loss = (50 - 40) = 10
So, there is a loss of Rs. 10.
Now, we will find the loss percentage, which is calculated as,
 $ \text{loss}\%=\dfrac{\text{loss}}{\text{cost price}}\times 100 $
Here, we have the loss = Rs. 10 and cost price = Rs. 50, so we get,
 $ \begin{align}
  & \text{loss}\%=\dfrac{10}{50}\times 100 \\
 & =\dfrac{100}{5} \\
 & =20\% \\
\end{align} $
Thus, we can say that there will be a loss of 20%. Hence, option (b) is the correct answer.

Note: The most common mistake that the students may make in this question is by assuming the value of the cost price of 40 articles as Rs. 40 and the selling price of 50 articles as Rs. 50. But this is not correct and will result in the wrong answer. Also, while finding the loss percentage, some students may use the wrong formula like, $ \text{loss}\%=\dfrac{\text{loss}}{\text{selling price}}\times 100 $ , but this is wrong, the correct formula is actually, $ \text{loss}\%=\dfrac{\text{loss}}{\text{cost price}}\times 100 $ .